How do you use the limit definition of the derivative to find the derivative of #f(x)=2/x#? Calculus Derivatives Limit Definition of Derivative 1 Answer Euan S. Jul 30, 2016 #f'(x) = -(2)/(x^2)# Explanation: #f'(x) = lim_(hrarr0) (f(x+h) - f(x))/h# #=lim_(hrarr0) (2/(x+h) - 2/x)/h = lim_(hrarr0) ((2x - 2(x+h))/(x(x+h)))/h# #=lim_(hrarr0)1/h (-2h)/(x(x+h)) = lim_(hrarr0) (-2)/(x(x+h)) = -(2)/(x^2)# Answer link Related questions What is the limit definition of the derivative of the function #y=f(x)# ? Ho do I use the limit definition of derivative to find #f'(x)# for #f(x)=3x^2+x# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(x+3)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/(1-x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=x^3-2# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/sqrt(x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=5x-9x^2# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(2+6x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=mx+b# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=c# ? See all questions in Limit Definition of Derivative Impact of this question 1218 views around the world You can reuse this answer Creative Commons License